Problem: Simplify the following expression: ${5(t+2)+3(1+4t)}$
Solution: Distribute the ${5}$ into the first set of parentheses: $ {5(}\gray{t+2}{)} + 3(1+4t) $ $ {5t+10} + 3(1+4t) $ Distribute the ${3}$ into the parentheses: $ 5t+10 + {3(}\gray{1+4t}{)} $ $ 5t+10 + {3+12t} $ Rewrite the expression to group the ${t}$ terms and numeric terms: $ {5t + 12t} + {10 + 3}$ Combine the ${t}$ terms: $ {17t} + {10 + 3}$ Combine the numeric terms: $ {17t} + {13}$ The simplified expression is $17t+13$